1. Field of the Invention
The present invention relates to a method and an apparatus for signal analysis. More specifically, the present invention relates to a method and an apparatus for signal analysis used not only in the speech related field such as extraction of fundamental frequency for speech analysis and synthesis but also in the field of extraction of periodicity of biological signals and diagnosis of machine vibration, for extracting fundamental frequency of periodic signals and almost periodic signals.
2. Description of the Background Art
It is desired to correctly find fundamental frequency of a periodic signal in the field of speech analysis, for example. However, satisfactory method has not yet been found. In a conventional method, based on a definition of periodic signal, a period T defined below is found, the reciprocal of which is regarded as the fundamental frequency. Here, p(t) is the periodic signal to be analyzed and neZ is an arbitrary integer. EQU p(t)=p(t+nT) (1)
Conventional method for obtaining period of such signal includes 1 time domain method, 2 frequency domain method, 3 auto correlation domain method and 4 a method of studying waveform singularity. Any of these methods cause some problem when applied to actual audio signals, and hence it has been generally believed that there is not a generally applicable universal method.
In time domain method (1), for example, a waveform is passed through a nonlinear circuit and then through a low pass filter, followed by extraction of a zero cross point or extraction of a peak position, to detect the period. In such a method, even when the period is roughly known in advance, much adjustment including setting of frequency of low pass filter or nonlinear circuit, method of detecting the peak and so on, and error derived from difference in signal level or spectrum shape has been unavoidable.
Representative one of the frequency domain method (2) is to extract a peak of cepstrum which is defined as a Fourier transform of logarithmic power spectrum. According to this method, if periodicity is perfect, correct period is obtained in principle. However, for the signals such as speech signal which is approximately periodical but has variation at each period, the method requires know-how to prevent various errors such as low peak, erroneous extraction of peaks caused by resonance such as speech formant, or erroneous taking of two periods as one.
Another problem, which is common to the method of auto correlation described below, is that it is necessary to increase time length of the signal used for analysis when the period is to be calculated precisely, and that the method cannot follow time change if the time change is fast as in the case of a speech, and further, when time window is made sufficiently short to follow the change, periodicity cannot be correctly extracted.
One method based on auto correlation (3) normalizes detailed power spectrum shape in accordance with global power spectrum shape using time windows of different lengths, modified auto correlation is calculated by inverse Fourier transform, and the signal period is calculated as the position of the peak thereof. However, as pointed out with respect to the cepstrum above, this method also suffers from similar problems concerning how to cope with fast changing period and where to tell global shape from detailed shape.
A method has been proposed which calculates, noting the fact that influence of global spectrum shape is removed from a residual signal obtained as a result of linear predictive analysis, the fundamental frequency from auto correlation of the residual signal. However, this method also suffers from the similar problem for fast changing signals.
The method of studying waveform singularity (4) assumes that a periodic signal is driven periodically by some event, which is the cause of periodicity, so that in this method, position of event is calculated to extract basic period and to find basic frequency. There is also a method noting phase of wavelet transformation as means therefor which is a relatively new method of signal analysis. However, in this method also, it is unclear what wavelet is to be used, and which of the detected signals is to be used for extracting fundamental period as a main event.
Because of these difficulties in principle, according to the conventional methods, a fraction of an integer or an integer multiple of an estimated value of the basic frequency may possibly be estimated erroneously as the fundamental frequency.